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MeteorologyWe reconstruct the meteorology at the South Col using observations from the automatic weather station (AWS) there (at 7945 m a.s.l)5 to downscale ERA5 reanalysis via a parsimonious blend of bias correction and machine learning. Initial screening indicates strong correlations between hourly ERA5 pressure level data bilinearly interpolated to South Col and air temperatures (r = 0.98), wind speed (r = 0.94), and relative humidity (r = 0.80) observed by the AWS. We therefore apply a simple empirical quantile mapping correction29 to remove systematic bias for these variables.Incident shortwave (SW) and longwave (LW) radiation are not available on ERA5 pressure levels, so we reconstruct them by downscaling the transmissivity (τ) and emissivity (α) of the atmosphere, defined:$$tau = {{{mathrm{SW/}}}}{Psi}$$
(1)
$${{{mathrm{and}}}};alpha = {{{mathrm{LW/}}}}sigma T_{{{mathrm{a}}}}^4$$
(2)
Where Ψ is the theoretical top of atmosphere solar radiation, σ is the Stefan Boltzmann constant (5.67 × 10−8 W m−2 K−4), and Ta is the 2 m air temperature (Kelvin). Observed values for τ and α are evaluated using AWS measurements of incident radiation and air temperature (using calculations of solar geometry to compute Ψ). We then train a Random Forest model (with 100 trees and a minimum leaf size of three) using Python’s Scikit Learn (version 0.20.1), modeling τ and α as a function of the ERA5 predictors in Methods Table 1. SW and LW could then be computed from:$${{{mathrm{SW}}}} = tau {Psi}$$
(3)
$${{{mathrm{LW}}}} = varepsilon T^4$$
(4)
Where T is the estimate from the bias-corrected ERA5 data.Table 1 Predictor variables used in the machine learning downscaling.Full size tableWe calibrate the bias correction and RF models using between 5012 (wind speed) and 12,810 (air temperature) overlapping hours of AWS observations and ERA5 data (May 2019 to December 2020). We evaluate the performance using a fivefold cross-validation, with results indicating very strong agreement between the observed and downscaled meteorology: hourly Pearson correlations range from 0.83 (relative humidity) to 0.98 (air temperature), translating respectively to root mean square errors between ~31 and 8% of the observed means (Supplementary Fig. 7). We also detect no sign of a seasonal dependence in the performance of bias correction and RF models (Supplementary Fig. 8). The resulting downscaled ERA5 data provide a complete annual series of hourly values for 1950–2019.We estimate precipitation at the South Col also using ERA5. First, we linearly interpolate the reanalysis data to the location of the Phortse AWS5 and then compute the ratio of the total observed precipitation (Po) and ERA5 precipitation (PE) during the overlapping period (April 2019-November 2020). We then multiply all reanalysis precipitation by this scalar to produce a corrected precipitation series (PE’) for Phortse 1950–2019:$$P_{{{mathrm{E}}}}^prime = frac{{P_{{{mathrm{o}}}}}}{{P_{{{mathrm{E}}}}}}P_{{{mathrm{E}}}}$$
(5)
To extrapolate to the South Col, we assume that precipitation decays exponentially with increasing elevation30. However, we recalibrate the regression using the Phortse and Basecamp AWSs because these new sites have weighing precipitation gauges protected by double alter shields5, and hence are less prone to under-catch error (Supplementary Fig. 9). Note that, as described below, the precipitation estimate is adjusted to an “effective” flux before being used to simulate glacier mass balance changes.Mass balanceWe use the precipitation, along with the other downscaled meteorological variables, to force the COSIPY model20 at hourly resolution for 1950–2019. First, we compute the effective precipitation (which implicitly includes the net effects of avalanching and wind transport, as well as correcting for any systematic bias in the downscaling/extrapolation method described above) required for the glacier to be in equilibrium for the period 1950–1959, iterating until the surface mass balance is zero. This is achieved when the precipitation is decreased by 65%. We then run two simulations with COSIPY. The first (referred to as the “snow” simulation) assumes a starting snowpack that is arbitrarily deep (20 m) to ensure that it remains present throughout the entire (70-year) simulation. We set the initial surface density of the snowpack to 350 kg m−3, the bottom density to 800 kg m−3, and linearly interpolate between. The second simulation (hereafter the “ice” simulation) uses the same effective precipitation but assumes no initial snowpack. However, snow is free to accumulate in the model in response to meteorological forcing. The algorithms and parameter values used in our application of COSIPY are outlined in Methods Table 2.Table 2 Parameterizations and parameter values used in the COSIPY model runs.Full size tableMeltThe surface melt rate depends on the surface energy balance (SEB):$$Q_{{{mathrm{h}}}} + Q_{{{mathrm{l}}}} + Q_{{{{mathrm{lw}}}}} + Q_{{{{mathrm{sw}}}}} + Q_{{{mathrm{g}}}} + Q_{{{mathrm{r}}}} – Q_{{{mathrm{m}}}} = 0$$
(6)
where Q denotes energy flux (W m−2) and the subscripts h, l, lw, sw, g, and r refer to the sensible, latent, net longwave radiative, net shortwave radiative, ground, and precipitation heat fluxes, respectively. The fluxes are defined as positive when directed towards the surface. The energy consumed in melting (Qm) is also defined as positive, meaning the melt rate (M; mm w.e. s−1 or kg s−1) can be calculated:$$M = frac{1}{{L_{{{mathrm{f}}}}}}mathop {sum}Hleft( {Q_{{{mathrm{m}}}},T_{{{mathrm{s}}}}} right)Q_i$$
(7)
in which H(Q,Ts) is a Heaviside function that returns a value of one unless both the sum of the first six terms in Eq. (6) (Qm = ∑Qi, with i indexing terms Qh to Qr) is positive and the surface temperature is also at the melting point; otherwise, it returns zero. The melt total over a period of ∆t seconds can then be expressed:$$M = Pfrac{{{Delta}t}}{{L_{{{mathrm{f}}}}}}{sum} {overline {Q_i} }$$
(8)
where P is the fraction of ∆t during which melting conditions occurred, and the overbar for energy component Qi indicates the mean value calculated during melting conditions. In terms of energy components Eq. (8) is the major driver of the amplification in melt totals between the snow and ice COSIPY simulations, increasing by a factor of 4.4; the energy sinks (sum of the remaining terms) amplify by a factor of 3.6 (Methods Fig. 3). The resulting amplification in mean melt rate (left( {acute{A} = frac{{left( {{sum} {overline {Q_i} } } right)_{{{{mathrm{ice}}}}}}}{{left( {{sum} {overline {Q_i} } } right)_{{{{mathrm{snow}}}}}}}} right)), though, is by almost a factor of 500. To understand this result, note that the proportional increase in melt rate can be written:$$acute{A} = frac{{koverline {Q_{{{{mathrm{sw}}}}}} – joverline {Q_{{{{mathrm{sinks}}}}}} }}{{overline {Q_{{{{mathrm{sw}}}}}} – overline {Q_{{{{mathrm{sinks}}}}}} }}$$
(9)
where (overline {Q_{{{{mathrm{sw}}}}}}) and (overline {Q_{{{{mathrm{sinks}}}}}}) are the mean energy gains and losses, respectively, during melt conditions in the snow simulation, and k and j are the proportional increases in these terms when transitioning to an ice surface (4.3 and 3.6, respectively). Critically, Eq. (9) reveals that (acute{A}) is inversely proportional to the baseline melt rate in the snow simulation (left( {overline {Q_{{{{mathrm{sw}}}}}} – overline {Q_{{{{mathrm{sinks}}}}}} } right)). The very low melt rate in the snow scenario (3.3 mm w.e. a−1), therefore acts to amplify the numerator of in Eq. (9).Sublimation and melt sensitivity to climate forcingTotal sublimation (S, mm w.e. or kg) can be written:$$S = rho ;U;C_{{{mathrm{e}}}}(e_{{{mathrm{s}}}} – e_{{{mathrm{a}}}}{Upsilon})frac{varepsilon }{{P_{{{mathrm{a}}}}}}{Delta}t$$
(10)
where ρ is the air density (kg m−3), U is the wind speed (m s−1), Ce is the turbulent exchange coefficient for moisture (dimensionless), ε is the ratio of gas constants for water vapor and air (0.622), Pa is air pressure (Pa), and Υ is relative humidity (fraction). The saturation vapor pressure for the surface (es) and the near-surface atmosphere (ea) are functions of the surface (Ts) and air temperature (Ta), respectively. If we assume that Ts = Ta (which is a reasonable simplification at the South Col where air temperature does not rise above 0 °C), and use the Clausius Clapeyron equation:$$e_{{{mathrm{s}}}} = e_0e^{frac{L}{{R_{{{mathrm{v}}}}}}left( { – frac{1}{{T_{{{mathrm{a}}}}}} + frac{1}{{273.15}}} right)}$$
(11)
in which e0 is the saturation vapor pressure at the melting point, L is the latent heat of sublimation (2.83 × 106 J kg−1), and Rv is the gas constant for moist air (461 J K−1); Eq. (10) becomes:$$S = rho ;U;C_{{{mathrm{e}}}}(1 – {Upsilon})e_0e^{frac{L}{{R_{{{mathrm{v}}}}}}left( { – frac{1}{{T_{{{mathrm{a}}}}}} + frac{1}{{273.15}}} right)}frac{varepsilon }{{P_{{{mathrm{a}}}}}}{Delta}t$$
(12)
which can be differentiated with respect to U, Ta, and Υ to explore the sensitivity of sublimation to changes in these meteorological parameters. In turn, the contribution of temporal trends (left( {frac{{{mathrm{d}}x}}{{{mathrm{d}}t}}} right)) in these variables to the trend sublimation can be evaluated via the chain rule:$$frac{{{mathrm{d}}S}}{{{mathrm{d}}t}} = frac{{partial S}}{{partial U}}frac{{{mathrm{d}}U}}{{{mathrm{d}}t}} + frac{{partial S}}{{partial Y}}frac{{{mathrm{d}}Y}}{{{mathrm{d}}t}} + frac{{partial S}}{{partial T_{{{mathrm{a}}}}}}frac{{{mathrm{d}}T_{{{mathrm{a}}}}}}{{{mathrm{d}}t}}$$
(13)
With:$$frac{{partial S}}{{partial U}} = rho ;C_{{{mathrm{e}}}};e_0left( {1 – {Upsilon}} right)e^{frac{L}{{R_{{{mathrm{v}}}}}}left( { – frac{1}{{T_{{{mathrm{a}}}}}} + frac{1}{{273.15}}} right)}frac{varepsilon }{{P_{{{mathrm{a}}}}}}{Delta}t$$
(14)
$$frac{{partial S}}{{partial T_{{{mathrm{a}}}}}} = L;C_{{{mathrm{e}}}};e_0;rho ;Uleft( {1 – {Upsilon}} right)frac{{e^{frac{L}{{R_{{{mathrm{v}}}}}}left( { – frac{1}{{T_{{{mathrm{a}}}}}} + frac{1}{{273.15}}} right)}}}{{R_{{{mathrm{v}}}}P_{{{mathrm{a}}}}T_{{{mathrm{a}}}}^2}}varepsilon {Delta}t$$
(15)
$$frac{{partial S}}{{partial {Upsilon}}} = – rho ;C_{{{mathrm{e}}}};e_0;Ue^{frac{L}{{R_{{{mathrm{v}}}}}}left( { – frac{1}{{T_{{{mathrm{a}}}}}} + frac{1}{{273.15}}} right)}frac{varepsilon }{{P_{{{mathrm{a}}}}}}{Delta}t$$
(16)
To evaluate Eq. (13) we compute the derivatives (Eqs. (14)–(16)) using the mean meteorology at the South Col during the ERA5 reconstruction (1950–2019), and ∆t to the number of seconds in 1 year (3.2 × 107 s). We prescribe the turbulent exchange coefficient (Ce) using the output from the COSIPY snow simulation, dividing the simulated sublimation by (rho ;U(e_{{{mathrm{s}}}} – e_{{{mathrm{a}}}}Upsilon )frac{varepsilon }{{P_{{{mathrm{a}}}}}}Delta t) (see Eq. (12)).Inserting these values into Eqs. (14) (16) yields:$$frac{{partial S}}{{dU}} = 6.0;{{{mathrm{mm}}}};{{{mathrm{w}}}}{{{mathrm{.e}}}}{{{mathrm{.}}}};{{{mathrm{a}}}}^{ – 1}{{{mathrm{m}}}}^{ – 1};{{{mathrm{s}}}}^1$$$$frac{{partial S}}{{d{Upsilon}}} = – 1.8;{{{mathrm{mm}}}};{{{mathrm{w}}}}{{{mathrm{.e}}}}{{{mathrm{.}}}};{{{mathrm{a}}}}^{ – 1}% ^{ – 1}$$$$frac{{partial S}}{{dT_{{{mathrm{a}}}}}} = 6.7,{{{mathrm{mm}}}},{{{mathrm{w}}}}{{{mathrm{.e}}}}{{{mathrm{.}}}},{{{mathrm{a}}}}^{ – 1},^circ {{{mathrm{C}}}}^{ – 1}$$We then estimate the time derivatives for Eq. (13) using the Theil-Sen slope estimation, yielding:$$frac{{{{d}}{U}}}{{{{d}}t}} = – 0.08;{mathrm{m}};{mathrm{s}}^{-1} ;{{{mathrm{decade}}}}^{ – 1};{{{mathrm{and}}}};frac{{partial S}}{{partial {U}}}frac{{{{d}}{U}}}{{{{d}}t}}; = ;0.05;{{{mathrm{mm}}}};{{{mathrm{w}}}}{{{mathrm{.e}}}}.;{{{mathrm{a}}}}^{ – 2}$$$$frac{{{{d}}{Upsilon}}}{{{{d}}t}} = – 0.6% ;{{{mathrm{decade}}}}^{ – 1};{{{mathrm{and}}}};frac{{partial S}}{{partial {Upsilon}}}frac{{{{d}}{Upsilon}}}{{{{d}}t}}; = ;0.11;{{{mathrm{mm}}}};{{{mathrm{w}}}}{{{mathrm{.e}}}}.;{{{mathrm{a}}}}^{ – 2}$$$$frac{{{{d}}T_a}}{{{{d}}t}} = 0.16;^circ {{{mathrm{C}}}};{{{mathrm{decade}}}}^{ – 1}{{{mathrm{and}}}};frac{{partial S}}{{partial T_{{{mathrm{a}}}}}}frac{{{{d}}T_{{{mathrm{a}}}}}}{{{{d}}t}}; = ;0.11;{{{mathrm{mm}}}};{{{mathrm{w}}}}{{{mathrm{.e}}}}{{{mathrm{.}}}};{{{mathrm{a}}}}^{ – 2}$$Summing these terms indicates a theoretical trend (left( {frac{{{mathrm{d}}S}}{{{mathrm{d}}t}}} right)) of 0.27 mm w.e. a−2, in reasonably close agreement with the 0.22 mm w.e. a−2 derived from the COSIPY snow simulation and reported in the main text. This theoretical analysis also indicates that 82% of the trend can be attributed to increasing air temperature (41%) and declining relative humidity (41%), with strengthening winds explaining the remaining 18%.An alternative (empirical) method to estimate the sensitivity of sublimation in the COSIPY snow simulation is to use multiple linear regression:$$S = alpha + beta _{{{mathrm{U}}}}U + beta _{{{mathrm{{Upsilon}}}}}{Upsilon} + beta _{T_{{{mathrm{a}}}}}T_{{{mathrm{a}}}}$$
(17)
Where the slope coefficients (βx) are linear approximations of the derivatives, relating the changes in the annual mean of the meteorological variables to the total annual sublimation. Performing the regression (Supplementary Fig. 11) lends support to the interpretation from the theoretical analysis above, attributing 49, 26, and 25% of the sublimation increase to the trends in air temperature relative humidity, and wind speed, respectively.In the main text, we highlight that sublimation and melt rates may differ in their response to climate forcing. To support this assertion, we repeat the sensitivity assessment above, evaluating the derivatives of the melt rate with respect to air temperature, wind speed, and relative humidity.We simplify the analysis by assuming that the proportion of time that the surface is melting (P) is constant (see Eq. (8)). Although physically incomplete, we note that there is no temporal trend in P for the COSIPY snow simulation (p  > 0.05 according to Seil-Then slope estimation). With this simplification, the sensitivity of the melt rate to changes in meteorological component x can then be written:$$frac{{{mathrm{d}}M}}{{{mathrm{d}}x}} = Pfrac{{{Delta}t}}{{L_{{{mathrm{f}}}}}}{sum} {frac{{partial underline {Q_i} }}{{partial x}}}$$
(18)
Wind speed, air temperature, and relative humidity appear in the expressions for the sensible, latent, and longwave heat fluxes (Qh, Ql, and Qlw, respectively):$$Q_h = rho ;U;c_{{{mathrm{p}}}};C_{{{mathrm{h}}}}(T_{{{mathrm{a}}}} – 273.15)$$
(19)
$$Q_l = rho ;U;C_{{{mathrm{e}}}};L_{{{mathrm{v}}}}({Upsilon}e_{{{mathrm{a}}}} – 611.3)frac{varepsilon }{{P_{{{mathrm{a}}}}}}$$
(20)
$$Q_{lw} = alpha sigma T_{{{mathrm{a}}}}^4 – 312.5$$
(21)
In which we have assumed melting conditions (Ts = 273.15, e0 = 611.3 Pa; Lv is the latent heat of vaporization [2.5 × 105 J kg−1], and the longwave thermal radiation emitted by the snow surface is 312.5 W m−2); cp is the specific heat content of the air (1004.7 J kg−1 K−1). It has been concluded31 that the incident longwave flux Qlw↓ in the Himalaya may be estimated from Υ and Ta:$$Q_{{{{mathrm{lw}}}}} downarrow = c_1 + c_2{Upsilon} + c_3sigma T_{{{mathrm{a}}}}^4 – 312$$
(22)
where the cx terms are empirically determined coefficients, whose value depends on cloudiness. Optimizing this expression for the South Col AWS, we found c1 = −17 (−168) W m−2, c2 = 0.73 (2.12) W m−2 %−1 and c3 = 0.57 (0.84) (dimensionless) for clear (cloudy) conditions.The derivative of these fluxes with respect to air temperature is then:$$frac{{partial Q_{{{mathrm{h}}}}}}{{partial T_{{{mathrm{a}}}}}} = rho ;U;c_{{{mathrm{p}}}};C_{{{mathrm{h}}}}$$
(23)
$$frac{{partial Q_{{{mathrm{l}}}}}}{{partial T_{{{mathrm{a}}}}}} = rho ;U;C_{{{mathrm{e}}}};L_{{{mathrm{v}}}};L;{Upsilon};varepsilon ;e_0frac{{e^{frac{L}{{R_{{{mathrm{v}}}}}}left( { – frac{1}{{T_{{{mathrm{a}}}}}} + frac{1}{{273.15}}} right)}}}{{R_{{{mathrm{v}}}}P_{{{mathrm{a}}}}T_{{{mathrm{a}}}}^2}}$$
(24)
$$frac{{partial Q_{{{{mathrm{lw}}}}}}}{{partial T_{{{mathrm{a}}}}}} = 4sigma c_3T_{{{mathrm{a}}}}^3$$
(25)
Note that all terms in Eqs. (23)–(25) are positive, outlining the physical basis for why melt rates should increase with rising air temperature32.The derivative of these fluxes with respect to relative humidity is:$$frac{{partial Q_{{{mathrm{l}}}}}}{{partial {Upsilon}}} = rho ;U;C_{{{mathrm{e}}}};L_{{{mathrm{v}}}};e_0e^{frac{L}{{R_{{{mathrm{v}}}}}}left( { – frac{1}{{T_{{{mathrm{a}}}}}} + frac{1}{{273.15}}} right)}frac{varepsilon }{{P_{{{mathrm{a}}}}}}$$
(26)
$$frac{{partial Q_{{{{mathrm{lw}}}}}}}{{partial {Upsilon}}} = c_2$$
(27)
Because all terms are positive in Eqs. (26) and (27), increases in relative humidity also drive increases in the melt rate.The derivatives of the sensible and latent heat fluxes with respect to wind speed are then:$$frac{{partial Q_{{{mathrm{h}}}}}}{{partial U}} = rho ;c_{{{mathrm{p}}}};C_{{{mathrm{h}}}}(T_{{{mathrm{a}}}} – 273.15)$$
(28)
$$frac{{partial Q_{{{mathrm{l}}}}}}{{partial U}} = rho ;C_{{{mathrm{e}}}};L_{{{mathrm{v}}}}frac{varepsilon }{{P_{{{mathrm{a}}}}}}(Ye_0e^{frac{L}{{R_{{{mathrm{v}}}}}}left( { – frac{1}{{T_{{{mathrm{a}}}}}} + frac{1}{{273.15}}} right)} – 611.3)$$
(29)
Because Ta is always less than 273.15 K during melt events at the South Col in the COSIPY snow simulation (Supplementary Fig. 12), (e_0;e^{frac{L}{{R_{{{mathrm{v}}}}}}left( { – frac{1}{{T_{{{mathrm{a}}}}}} + frac{1}{{273.15}}} right)}) must be less than 611.3 Pa. Hence, the last terms in Eqs. (28) and (29) are negative, and so increases in wind speed act to reduce the melt rate.In summary, then, theory indicates that rising air temperatures should accelerate both sublimation and melt rates (Eqs. (15) and (24)). However, increases in wind speed and relative humidity will have opposite effects. Due to the persistence of freezing air temperatures during surface melt events, faster winds act to enhance sublimation (Eq. (14)) but reduce melting (Eqs. (28) and (29)), whereas increasing relative humidity amplifies melting (Eqs. (26) and (27)) but dampens sublimation (Eq. (16)). More

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The global co-occurrence of freshwater stress and freshwater storage trendsWe mapped freshwater stress and trends in freshwater storage at the basin scale and analyzed the co-occurrence of these phenomena (Fig. 1).Fig. 1: Global co-occurrence of freshwater stress and storage trends.a Freshwater stress, derived from freshwater withdrawal and streamflow datasets (see “Methods” section). b Freshwater storage trend per basin. c Combinations of freshwater stress and storage trend per basin, which together derive basin freshwater status (shown in Fig. 2b). Values overlaying the legend indicate the number of basins satisfying each set of conditions. For categorical plotting purposes only, ±3 mm year−1 is used as the threshold denoting a clear directional storage trend, based on the error level of the underlying observations25. d–g The exposure of social-ecological activity to freshwater stress and storage trends. Each plot represents storage trends as the x-axis coordinate, and log-transformed freshwater stress as the y-axis coordinate with the size of each circle based on the basin’s value respective to each plotting dimension.Full size imageFreshwater stress represents the state of demand-driven water scarcity15 and is defined as the ratio of freshwater withdrawal to streamflow (Fig. 1a). Trends in freshwater storage, conversely, represent the evolution of total storage, defined as the vertical sum of groundwater, soil moisture, surface water, and snow water equivalent storages (Fig. 1b). Freshwater stress and storage are linked, as freshwater storage becomes a required source of water during periods when demands exceed supply. As climate change intensifies hydrological extremes globally, the strategic importance of the world’s largest store of liquid freshwater, groundwater, will only continue to increase24. Though studies have focussed on global assessments of freshwater stress13,14,15 and trends in freshwater storage9, no study to date has mapped these two variables against one another. Doing so provides important context to differentiate basins of equal freshwater stress, as drying trends are likely to exacerbate challenges derived from freshwater stress, while wetting trends may yield offsetting effects. However, as freshwater stress calculations do not differentiate between withdrawals sourced from streamflow or storage, the two variables are not necessarily independent.We found that 201 (42%) of the 478 currently stressed basins (withdrawal/streamflow > 0.10) are simultaneously losing freshwater storage (Fig. 1c). These basins are located in south and southwestern USA, northeastern Brazil, central Argentina, Algeria, and concentrate throughout the Middle East, the Caucasus, northern India, and northern China. Predominantly, these regions are agriculturally significant and heavily irrigated9, with the exception of a few basins in South America whose trends are likely the product of natural variability9. Conversely, 98 (21%) of the currently stressed basins are gaining freshwater storage. The storage trends in these basins have largely been attributed to natural variability with the exception of central India, whose trends are partially attributed to groundwater recovery following groundwater policy change9. The remaining 179 stressed basins have freshwater storage trends that are smaller than can be definitively interpreted from the satellites monitoring these trends25. This skew towards negative storage trends (i.e., drying) in the world’s water-stressed basins dissipates and even reverses in the non-stressed basins, where drying and wetting trends are found in 23% and 32% of the 726 non-stressed basins, respectively. While previous work has shown that the world’s dry regions are becoming drier while the wet regions are becoming wetter26, this work reveals that the stressed regions of the world are becoming drier while the non-stressed regions of the world have no clear overall trend in freshwater storage.The encompassed human population, food crop production, gross domestic product (GDP), biodiversity, and wetlands enumerate the potential social-ecological impacts from the current state of global freshwater stress and storage trends. Around 2.2 billion people, 27% of global food crop production, and 28% of global GDP live, grow, and situate in freshwater stressed basins that are drying (Fig. 1d–f). These totals represent an upper limit as not all social and ecological activity within these basins will be affected by freshwater stress and storage loss, which will depend on local levels of adaptive capacity and ecological sensitivity22 (our focus in the subsequent sections). Conversely, 1.2 billion people, 24% of global food crop production, and 19% of global GDP are found in stressed basins that are wetting. We find less taxonomic biodiversity in the freshwater stressed and drying basins, and greater biodiversity in unstressed and wetting basins. Roughly the same number of wetlands of international importance are found in stressed and drying basins as in stressed and wetting basins. While these totals represent the magnitude of potentially affected biodiversity and wetlands, taxonomic biodiversity is only one of many critical facets of biodiversity27, and freshwater stress and storage trends are but two of many variables impacting global biodiversity28. Thus, we urge caution in interpreting the role of freshwater stress and storage in driving differences in these biodiversity distributions.The most vulnerable populations to freshwater stress and storage lossTo better characterize social vulnerability, freshwater stress and storage loss must be placed in the context of social adaptability. We mapped and analyzed the co-occurrence of freshwater stress and storage trends with an existing global dataset of social adaptive capacity23 summarized at the basin scale (Fig. 2). Social adaptive capacity (Fig. 2a), or adaptability, represents “the ability of the system to respond to disturbances”29 and is derived based on input indicators of governance, economic strength, and human development. This consideration of social adaptability enables more representative estimates of social, agricultural, and economic activity that are vulnerable to the co-occurrence of freshwater stress and storage loss. To consider freshwater stress and storage loss together, we developed the basin freshwater status indicator (Box 1) where higher values indicate co-occurring freshwater stress and storage loss (Fig. 2b, see “Methods” section).Fig. 2: The relationship between basin freshwater status and social adaptive capacity.a Social adaptive capacity, or adaptability, per basin. b Basin freshwater status, representing the combination of freshwater stress and storage trend per basin (see “Methods” section). c Combinations of basin freshwater status and social adaptability. Values overlaying the legend indicate the number of basins satisfying each set of conditions. d–g The exposure of social-ecological activity to basin freshwater status (x-axis coordinate) and social adaptive capacity (y-axis coordinate), with the size of each circle scaled based on the basin’s value respective to each plotting dimension. These distributions are summarized below each plot. P notation represents the percentile distribution.Full size imageWe found 73 basins to possess low levels of social adaptability and severe basin freshwater status (Fig. 2c). These basins concentrate in Northern, and Eastern Africa, the Arabian Peninsula, and Western, Central, and Southern Asia; although vulnerable basins are also found in northeast Brazil, Southern Africa, and northern China. These basins encompass approximately 1.2 billion people, 12% of global food crop production, and 6% of global GDP (Fig. 2d–f). Conversely, 119 and 49 basins are found to have similarly severe basin freshwater status yet have moderate or high levels of social adaptability, respectively. These basins are located in southwestern USA and Mexico, Chile and Argentina, the Arabian Peninsula, regions surrounding the Caspian Sea, western Australia, and the North China Plain.These differences in social adaptability across basins with severe freshwater status (i.e., co-occurring freshwater stress and storage loss) raise important economic considerations. First, greater social adaptability likely coincides with greater technological and economic capacity to pursue development. This development may consume greater volumes of freshwater and drive basins towards greater levels of freshwater stress or storage loss, while simultaneously increasing institutional and technical capacity to cope with limited water resources. Furthermore, freshwater stress and storage loss are not certain to induce negative economic impacts on basins, and can lead to positive impacts if a region is able to leverage its comparative advantages (e.g., irrigation efficiency) among other stressed regions30. Second, the divergent economic situation facing basins with severe freshwater status is particularly evident on a per-capita basis. In severe freshwater status, low adaptability basins, there resides 17% of the global population yet only 6% of global GDP. Conversely, in severe freshwater status basins with moderate-and-greater social adaptability, there resides 14% of the global population and an outsized 18% of global GDP (Fig. 2d, f). It is thus paramount that global initiatives prioritize and link economic inequality with freshwater goals. One such example is Sustainable Development Goal (SDG) 6.4 (“reduce the number of people suffering from water scarcity”), which we argue should increasingly be linked to targets of SDG 10 (“reduce inequality within and among countries”).Box 1 Key terminology as used in this paper. See Methods for further informationFreshwater stress: The ratio of annual freshwater withdrawal (W) to annual streamflow (Q). We refer to basins with W/Q ≥ 10% as stressed basins and those with W/Q ≥ 40% as highly stressed basins.Freshwater storage trends: Year-over-year trends in total freshwater storage based on satellite observations over the 2002–2016 time period. Total freshwater storage is a vertically aggregated measure of water storage that includes groundwater, soil water, surface water, canopy water, and ice and snow water equivalents where present. For simplicity, we refer to negative freshwater storage trends as drying trends or storage loss and positive trends as wetting trends or storage gain.Basin freshwater status: An integrated indicator that combines normalized freshwater stress and normalized freshwater storage trends at the basin scale. High indicator scores are assigned to basins with co-occurring freshwater stress and drying trends. We refer to high freshwater status scores through status severity.Vulnerability: The likelihood of society and ecosystems to experience harms due to exposure to freshwater stress and storage loss when considered together as a basin’s freshwater status. This vulnerability definition is an application of Turner et al.’s generic definition29. Vulnerability is quantified using social adaptability, ecological sensitivity, and basin freshwater status indicators. Social adaptability and ecological sensitivity indicators are described in the text and Methods.Hotspot basin: Highlighted basins that possess the greatest vulnerability scores. We identify hotspot basins to support their prioritization in global water resources and integrated management initiatives. Basins are considered hotspots if sorted into “high” and “very high” vulnerability classes following a categorical classification of the numerical vulnerability results.Hotspot basins found on all continentsWe mapped the global gradient in social-ecological vulnerability to freshwater stress and storage loss at the basin scale and, from this, identified those with the greatest vulnerability as hotspot basins (Fig. 3). Hotspot mapping has been a successful endeavor within the field of conservation biogeography31,32, and many global hydrology studies have identified regions of exceptional water scarcity and security challenges e.g.,13,14,15,17,18,19. Here, we seek to combine and apply these concepts in an integrated global social-ecological vulnerability context. As a useful reference, biodiversity hotspots aim to “maximize the number of species “saved” given available resources” by asking “where are places rich in species and under threat?”33. For comparison, the aim of our hotspot mapping is to ‘minimize the social and ecological impacts of freshwater stress and storage loss given available resources’ by asking “what basins with sensitive ecosystems and limited social adaptive capacity are exposed to freshwater stress and storage loss?”Fig. 3: Hotspot basins for social and ecological impacts from freshwater stress and storage loss.a–d Social-ecological vulnerability results. a Hotspot basins of social-ecological vulnerability to freshwater stress and storage loss. b Vulnerability classification, based on the product of basin freshwater status and social-ecological sensitivity to freshwater stress and storage loss (see “Methods” section). c Histograms of the global distribution of vulnerability classes by basin count and surface area. d Summarized social-ecological activity within transitional and hotspot basins. e Ecological vulnerability results, presented as vulnerability classes. f Social vulnerability results, presented as vulnerability classes. Vulnerability classes for e and f are derived using the same methods as shown for social-ecological vulnerability in b.Full size imageWe conceptualize vulnerability as the product of (i) ecological sensitivity, (ii) social adaptive capacity, and (iii) basin freshwater status. To represent ecological sensitivity, we derived an indicator using data products from two global ecohydrological studies that assess broad ecosystem sensitivity to freshwater storage and use (see “Methods” section). To represent social adaptability, we utilized the same adaptive capacity dataset as used in the previous section (Fig. 2a). To classify the derived global vulnerability results into hotspot basins, we implemented a simple classification algorithm developed for heavy-tailed distributions34, which appropriately describes the global vulnerability distribution.The most vulnerable basins are constrained to regions confronting co-occurring freshwater stress and storage loss. When considering social and ecological vulnerability individually (Fig. 3e, f), we find spatial variation between ecological vulnerability (Fig. 3e) and social vulnerability (Fig. 3f). For instance, several basins in affluent nations with sensitive ecosystems reveal high ecological vulnerability but low social vulnerability (southwestern USA; western Australia). Conversely, several basins in Eastern Africa and northeastern India possess high social vulnerability but low to moderate ecological vulnerability. While these differences are notable and could impact regional strategies, it remains essential in most, if not all, regions that social and ecological vulnerabilities be confronted simultaneously4. For this purpose, we combined ecological sensitivity and adaptive capacity indicators into a combined social-ecological sensitivity indicator (see “Methods” section) to map combined social-ecological vulnerability (Fig. 3a).We identify 168 basins, representing 14% of all basins and 11% of the global land area considered in our study, as vulnerability hotspots (Fig. 3a–c). These hotspot basins consist of basins receiving “high” and “very high” vulnerability scores through our classification procedure. Of the 168 basins, 78 (6% of all basins) are classified in the most-severe “very high” vulnerability class, while 90 (7% of all basins) are classified in the “high” vulnerability class. We also identified 232 basins (19% of all basins) as “transitional” basins, which are not classified alongside basins with null vulnerability yet also do not possess extreme values within the global vulnerability distribution. The 78 hotspot basins with “very high” vulnerability represent the multiple epicenters for potential social and ecosystem impacts from freshwater stress and storage loss. These basins are found in Argentina, northeastern Brazil, the American southwest, Mexico, Northern, Eastern, and Southern Africa, the Middle East and Arabian Peninsula, the Caucasus, West Asia, northern India and Pakistan, Southeastern Asia, and northern China.A total of over 1.5 billion people, 17% of global food crop production, and 13% of global GDP are found within hotspot basins (Fig. 3d). Of these, ~300 million people, 4% of global food crop production, and 4% of global GDP situate within the 78 “very high” vulnerability basins. Consistent with the relationship between biodiversity and basin freshwater status, we find the most vulnerable basins to be less taxonomically biodiverse than less vulnerable basins. While it is possible that these lower biodiversity levels may have eroded due to freshwater stress and storage loss, a proper investigation is outside the scope of this study and would require a wider array of pressures to be considered. The hotspot basins encompass 157 wetlands of international importance, which we highlight to prioritize their conservation in these vulnerable environments (Supplementary Table 2).While the degree of social-ecological activity within hotspot basins is substantial, the global proportion of each dimension found in hotspot basins is roughly proportional to the fraction of basins within each vulnerability class. Thus, as the hotspot basins do not contribute disproportionately to global totals of social-ecological activity, we find it important to restate and clarify the motivating purpose of this hotspot mapping. The hotspot basins do not identify the greatest contributors to global social-ecological activity that face severe freshwater challenges. Rather, the hotspot basins are those with sensitive ecosystems and adaptability-limited societies exposed to the co-occurrence of freshwater stress and storage loss, and thus are the basins most likely to suffer social and ecological harms due to these freshwater conditions.The identification of hotspot basins shows high levels of consistency across two uncertainty analyses and a sensitivity analysis focused on the impacts of subjective methodological decisions (Supplementary Section 4). We consider individually the impacts of (i) uniform over-estimation and under-estimation of each data input (spatially uniform uncertainty) and (ii) heterogeneous uncertainty in each data input (spatially variable uncertainty) on our hotspot basin results. Performing 10,000 realizations for each uncertainty analysis, we find that 98% of the identified transitional and hotspot basins are identified as at least transitional basins in over 50% the realizations considering spatially uniform uncertainty, and 96% when considering spatially variable uncertainty (Supplementary Figs. 8 and 9). The subjectivity-focused sensitivity analysis considered 24 alternative methodological configurations, and revealed that our identified transitional and hotspot basins are consistently identified across the majority of configurations (Supplementary Fig. 10).Implementation of integrated water resources management is inconsistent across hotspot basinsWe compared national implementation levels of integrated water resources management (IWRM) with our global vulnerability results (Fig. 4). For IWRM implementation data, we rely on the IWRM Data Portal35 which tracks progress on SDG 6.5.1 (“IWRM implementation at the national scale”).Fig. 4: Integrated water resources management in hotspot basins.a Map of IWRM implementation overlaid by hotspot basin results. b Scatterplot of individual basin values of social-ecological vulnerability (x-axis) and IWRM implementation (y-axis). Transboundary basins are represented by concentric red circles, with the number of circles representing the number of nations present within each basin. See text for interpretation of labels 1, 2, and 3.Full size imageIWRM is defined as “a process which promotes the co-ordinated development and management of water, land and related resources, in order to maximize the resultant economic and social welfare in an equitable manner without compromising the sustainability of vital ecosystems”36, while the SDG framework notes that IWRM implementation “supports all Goals across the 2030 Agenda”37. Thus, as the IWRM paradigm seeks to guide management of water resources to minimize trade-offs between human well-being, ecological health, and water resources sustainability, assessing implementation levels of IWRM against our vulnerability results provides insight regarding the performance of IWRM globally while simultaneously emphasizing the broad sustainability implications within hotspot basins.Globally, we find no direct relationship between vulnerability and IWRM implementation at the basin scale. There is thus a wide range of IWRM implementation across all levels of social-ecological vulnerability to freshwater stress and storage loss, and there is no indication that IWRM implementation levels are greatest where they are most needed. This finding likely derives from variations in proactive versus reactive governance and management approaches to freshwater challenges across the globe. As our analysis is conducted at a snapshot in time (input data align to ~2015), we can only generate hypotheses about the performance of IWRM globally. For example, basins with high levels of IWRM implementation and low vulnerability (label 1 in Fig. 4b) have either proactively implemented IWRM, have effectively reduced their vulnerability through IWRM implementation, or simply benefit from a favorable intersection of regional climate and economy.Alternatively, basins with low levels of IWRM and low vulnerability can be categorized as non-proactive in their IWRM implementation (label 2 in Fig. 4b). We place particular emphasis here on basins with low levels of IWRM where vulnerability is high (label 3 in Fig. 4b), which we argue should be the priority basins and regions of SDG 6.5-focused initiatives. Identified nations with low levels of IWRM implementation and very high vulnerability include Afghanistan, Algeria, Argentina, Egypt, India, Iraq, Kazakhstan, Mexico, Somalia, Ukraine, Uzbekistan, and Yemen. As one-third (36%) of all hotspot basins are transboundary (Fig. 4b), improving basin-level IWRM implementation will require multilateralism and hydro-diplomacy and cannot be left to individual nations acting alone. Furthermore, we observe a lower level of IWRM implementation across hotspot basins that are transboundary versus non-transboundary hotspot basins (mean basin IWRM Data Portal score = 50 vs. 56), suggesting greater multilateralism and cooperation are needed in transboundary basins. More

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Catchment locations and input dataTo determine the impact of afforestation on catchment hydrology we select twelve varied catchments from across the British Isles (Supplementary Material-S1 and Fig. 1). These catchments capture a range of hydrological regimes, drainage patterns and catchment soil and land-cover properties to determine how such factors may influence catchment response to afforestation. Being predominantly >1000 km2 in area (ranging from 511 to 9931 km2 in size), they are adequately represented in a hydrological model to integrate processes at a 1 km2 spatial resolution54,55. Two catchments are nested within larger ones, the Ure within the Ouse, and the Severn at Bewdley (Severn-B) within the Severn at Haw Bridge (Severn-HB) (Fig. 1).The period 2000–2010, a flood-rich period for the British Isles36,37, is chosen to assess afforestation influence on streamflow as it allows us to avoid the uncertainty that would be associated with land-cover changes over a longer period when comparing to baseline results. This length of the simulation period also reduces the computational demand with a large ensemble of land-cover scenarios. Accordingly, the CEH land-cover map for the year 200056, in the form of the CHESS-land dataset57, is used to provide configurational datasets specifying soil hydraulic and thermal properties, vegetation characteristics, and orography, for the model at a 1 km2 spatial resolution for the unaltered land-cover scenarios. This dataset has successfully been used in other studies55,58. The 25 m rasterised land-cover map is reclassified into eight different land-cover types (Supplementary Tables S4 and S5) and used to derive afforestation scenarios related to land cover before being converted to a percentage land-cover fraction at a 1 km2 spatial resolution. To provide the required meteorological driving data, we use the CHESS-met dataset59 which includes long-wave and short-wave radiation, air temperature, specific humidity and pressure. The 50 m CEH Integrated Hydrological Digital Terrain Model elevation data is used to derive topographical and catchment attributes as well as catchment boundaries and river networks60. Soil hydraulic information comes from the Harmonised World Soil Database and was made uniform across each grid cell61.The modelThe Joint UK Land Environment Simulator (JULES) is a physically based land-surface model that simulates the fluxes of carbon, water and energy at the land surface when driven by a time series of the atmospheric data23,24. Multiple studies have used JULES before including the investigation into evapotranspiration drivers across Great Britain58,62, atmospheric river formation over Europe63, the impact of solar dimming and carbon dioxide on runoff64 and developing river routing algorithms with a Regional Climate Model65. JULES is routinely used at the Met Office, where it is coupled with several other models to understand future changes globally and across the UK, by bridging the atmosphere, land surface and ocean66. This study is predominantly a theoretical, scenario-based modelling study designed to draw out general principles and to quantify the relation between afforestation and hydrological response, and as such the results are not intended to provide detailed guidance for specific practical actions.The use of a process-based model enables us to investigate physical explanations for the hydrological impacts of changes in land cover and the explicit representation of vegetation that will influence fluxes, partitioning and storages within the realm of epistemic uncertainty for other conceptual and hydrological models where vegetation is not included. JULES models both plant phenology and canopy storages23,24. When changing the plant functional type in JULES, both the properties of the above-ground vegetation (such as canopy height and leaf area index) and the soil infiltration factor and the root depth are altered23. However, there are several caveats that must be considered with this approach. First, the model configuration used in the present study is uncoupled from the atmosphere and so large-scale land-cover changes cannot alter nearby weather67. Second, each grid cell is hydrologically separated from adjacent cells, with streamflow and runoff hydrologically uncoupled from the rest of the system. Soil water also does not flow between grid cells. Third, soil thermal and hydraulic properties are uniform across a grid cell. This reduces the impact of hydrological pathways within a cell and the interaction of vegetation with these varying soil types that could have ramifications at multiple temporal and spatial scales. For example, within the cell there may be vegetation that is water-stressed (e.g. valley sides) compared with vegetation where water is not limited (e.g. floodplain) which would change how much transpiration is possible and thus runoff68.Precipitation in the model is partitioned by vegetation and when it reaches the soil surface it is portioned into either infiltration excess overland flow, at a rate controlled by the hydraulic conductivity of the soil, or saturation-excess overland flow as determined by the Probability Distributed Model (PDM)69,70. Throughfall (TF) through the canopy is dependent on the rainfall and the existing water in the canopy:$${T}_{F}=Pleft(1-frac{C}{{C}_{m}}right)exp left(-frac{{varepsilon }_{r}{C}_{m}}{PvarDelta t}right)+Pfrac{C}{{C}_{m}}$$
(1)
where P is the rainfall rate (kg m−2 s−1), C is the amount of water in the canopy (mm), Cm is the maximum water storage of the canopy (mm) and εr is the fraction of the grid cell occupied by convective precipitation. The maximum amount of canopy water storage is a function of the leaf area index (L):$${C}_{m}={A}_{m}+{B}_{m}L$$
(2)
where Am is the ponding of water on the soil surface and interception by leafless vegetation (mm) and Bm is the rate of change of water holding capacity with leaf area index. At each timestep (n) the canopy storage is updated thus:$${C}^{(n+1)}={C}^{(n)}+(P-{T}_{F})Delta t$$
(3)
Based on the surface energy balance, the fraction of the proportion of water stored in the canopy compared with the maximum canopy capacity of that plant type is used to calculate the effective surface resistance to determine tile evapotranspiration.Surface runoff is generated by two processes in JULES: infiltration excess, where the water flux at the surface is greater than the infiltration rate of the soil, and saturated excess overland flow where the water flux at the surface is converted to runoff when the soil is completely saturated. To calculate the saturation-excess overland flow, the PDM69 is used to determine the fraction of the model grid cell that will be saturated (fsat) which is used as a multiplier to convert any excess water reaching the surface to runoff:$${f}_{{{{{{mathrm{sat}}}}}}}=1-{left[frac{{max }(0,S-{S}_{0})}{{S}_{{max }}-{S}_{0}}right]}^{frac{b}{b-1}}$$
(4)
where S is the fraction of the grid cell soil water storage, S0 is the minimum storage at and below which there is no surface saturation (mm), Smax is the maximum grid cell storage (mm) and b is the Clapp and Hornberger71 soil exponent. We use the topography-derived parameterisation for the b and S0/Smax parameters to reduce individual calibration with the following relationship55:$$left{begin{array}{c}b=2.0hfill\ {S}_{0}/{S}_{{max }}=,{max },(1-frac{s}{{s}_{{max }}},,0.0)end{array}right.$$
(5)
where s is the grid cell slope (°) and smax is the maximum grid cell storage (mm). Once interception and surface runoff have been calculated, the remaining water enters the soil. This water is allocated to the different soil layers within the soil column by using the Darcy–Richards equation:$$W=kleft(frac{{{{{{mathrm{d}}}}}}varphi }{{{{{{mathrm{d}}}}}}z}+1right)$$
(6)
where W is the vertical flux of water through the soil (kg m−2 s−1), k is soil conductivity (kg m−2 s−1), φ is suction (m) and z is the vertical flux of water through the soil (m). To calculate suction and soil conductivity, we use the van Genuchten72 scheme:$$left(frac{theta }{{theta }_{s}}right)=frac{1}{{[1+{(alpha varphi )}^{(frac{1}{1-m})}]}^{m}}$$
(7)
where θ is the average volumetric soil moisture (m3 m−3), θs is the soil moisture at saturation (m3 m−3), α and m are van Genuchten parameters dependent on soil type. The hydraulic conductivity is calculated thus:$${K}_{h}={K}_{hs}{S}^{varepsilon }{left[1-{left(1-{S}^{frac{1}{m}}right)}^{m}right]}^{2}$$
(8)
where Kh is the hydraulic conductivity (m s−1) and Khs is the hydraulic conductivity for saturated soil (m s−1). ε is an empirical value set at 0.5 in JULES and S is found by:$$S=frac{(theta -{theta }_{r})}{({theta }_{s}-{theta }_{r})}$$
(9)
where θr is the residual soil moisture (m3 m−3). Vegetation can access water from each level in the soil column as a function of the root density where the fraction of roots (r) in each soil layer (l) from depth zl-1 to zl is:$${r}_{l}=frac{{e}^{-frac{2{z}_{l-1}}{{d}_{r}}}-{e}^{-frac{2{z}_{l}}{{d}_{r}}}}{1-{e}^{-frac{2{z}_{t}}{{d}_{r}}}}$$
(10)
where zl is the depth of the lth soil layer, dr is the root depth (m) and zt is the total depth of the soil column (m). The water flux extracted from a soil layer is elE where E is transpiration (kg m−2 s−1) and el can be found by:$${e}_{l}=frac{{r}_{l}{beta }_{l}}{{sum }_{l}{r}_{l}{beta }_{l}}$$
(11)
and βl is defined by:$${beta }_{l}=left{begin{array}{cc}1 hfill& {theta }_{l}ge {theta }_{c}hfill\ ({theta }_{l}-{theta }_{w})/({theta }_{c}-{theta }_{w}) & {theta }_{w}, < ,{theta }_{l} , < , {theta }_{c}hfill\ 0 hfill& {theta }_{l}le {theta }_{w}hfillend{array}right.$$ (12) where θc and θw are the volumetric soil moisture critical and wilting points respectively (m3 m−3) and θl is the unfrozen soil moisture at that soil layer (m3 m−3). In this configuration of JULES, when a soil layer becomes saturated, the excess water is routed to lower layers. When the bottom layer becomes fully saturated any excess water is added to the subsurface runoff. Both the surface and subsurface runoff are then passed to the River Flow Model65,73 which routes the flows according to a flow direction grid74.This study uses a combination of calibrated model parameters from the previous work of Robinson et al.59 and Martinez-de la Torre et al.55 (Rose suites u-bi090 and u-au394, respectively, which can be found using the Rose/Cylc suite control system: https://metomi.github.io/rose/doc/html/index.html). We compare observed streamflow from the NRFA database75 with model output for the years 2000–2010 using the base land and CHESS-met datasets. The model is spun-up for the years 1990–2000 to ensure soil moisture content has been equilibrised. To quantify the accuracy of the model, we use a range of standard error metrics. These include the Nash–Sutcliffe efficiency76 measure:$${{{{{mathrm{NSE}}}}}}=1-frac{{sum }_{i=1}^{n}{({Q}_{{{{{{mathrm{sim}}}}}}}-{Q}_{{{{{{mathrm{obs}}}}}}})}^{2}}{{sum }_{i=1}^{n}{({Q}_{{{{{{mathrm{obs}}}}}}}-{bar{Q}}_{{{{{{mathrm{obs}}}}}}})}^{2}}$$ (13) Kling–Gupta efficiency77:$${{{{{mathrm{KGE}}}}}}=1-sqrt{{(r-1)}^{2}+{left(frac{{sigma }_{{{{{{mathrm{sim}}}}}}}}{{sigma }_{{{{{{mathrm{obs}}}}}}}}-1right)}^{2}+{left(frac{{mu }_{{{{{{mathrm{sim}}}}}}}}{{mu }_{{{{{{mathrm{obs}}}}}}}}-1right)}^{2}}$$ (14) Root-mean-squared error:$${{{{{mathrm{RMSE}}}}}}=sqrt{mathop{sum }limits_{i=1}^{n}{({Q}_{{{{{{mathrm{sim}}}}}}}-{Q}_{{{{{{mathrm{obs}}}}}}})}^{2}}$$ (15) Mean absolute error:$${{{{{mathrm{MAE}}}}}}=frac{{sum }_{i=1}^{n}|{Q}_{{{{{{mathrm{sim}}}}}}}-{Q}_{{{{{{mathrm{obs}}}}}}}|}{n}$$ (16) where Qsim is the simulated discharge, Qobs is the observed discharge, r is the linear correlation between observation and simulations, σsim|obs is the standard deviation of discharge, μsim|obs is the mean of discharge and n is the number of observations. We also use NSE(log(Q)) and KGE(1/Q) to understand how well the model can reproduce low flows. Using these measures, we find that JULES performs satisfactorily apart from the Avon Catchment which may be due to fast subsurface flows generated by its geology55 (Supplementary Table S7). With process-based models, it is difficult to both accurately reproduce physical processes and make the output faithful to reality due to epistemic uncertainties78. Even though model performance is not the same as achieved with calibrated conceptual or empirical models, it allows us to determine the effects of vegetation changes on the hydrological cycle.JULES’ ability to faithfully represent hydrological land-surface processes in Great Britain has been evaluated in several studies58,79,80 and the plant functional type parameters it uses at global scales81,82. To validate the ability of our configuration of JULES to represent soil moisture and potential evapotranspiration rates, we compare the model output with observations from twelve COSMOS-UK sites within our catchments covering grasslands, croplands, coniferous and broadleaf woodland83 (Supplementary Fig. S8). We evaluate model performance from the start of the COSMOS-UK station records until January 1, 2018 so that we use the same forcing data as our experiments. Station start dates vary from October 2013 to August 2017. We compare COSMOS-UK observed soil moisture to the first 0.1 m of the soil column in JULES and evaporation to the sum of the soil evaporation and plant transpiration. We find a median KGE score of 0.44 for the topsoil moisture and 0.53 for potential evaporation (Supplementary Tables S9 and S10). Low error metrics observed for topsoil moisture are due to systematic undercalculation by JULES80. At our broadleaf sites, Alice Holt and Wytham Woods, we find both systematic over and underprediction of the topsoil moisture respectively. In line with other studies, we find that there is a slight overestimation of evaporation in JULES58,84. As illustrated by the median coefficients of determination between the COSMOS-UK and JULES data of 0.62 and 0.60 for the topsoil moisture and evaporation respectively, JULES broadly represents changes in these variables over time.Land-cover scenariosModelling the influence of afforestation on catchment hydrology has been attempted before but usually only at the scale of a single catchment for a limited range of scenarios. In this study, we focus on the theoretical effect of widespread planting of broadleaf trees to examine whether planting location is a stronger control on hydrological response than afforestation extent by using a large ensemble of up to 288 land-cover change scenarios. We choose to focus just on broadleaf woodland for several reasons. First, we are trying to replicate a landscape that could be considered a natural climatic climax community that might occur if it had not been for human intervention during the Holocene. Second, broadleaf woodland has the potential to absorb and store carbon in soils for longer time periods. Finally, to reduce computational cost and the issue of potentially expanding the errors induced by potentially spurious parameters of needleleaf woodland in this version of JULES85. Although potential woodland planting locations have been suggested by the Environment Agency and authorities in Scotland and Wales86,87,88, the differences in planting criteria means it is not possible to systematically compare hydrological changes across our chosen catchments. Here we attempt to create afforestation scenarios related to both catchment river network structure and land use that are directly comparable across a range of catchments. Afforestation was in grassland areas to reduce the complexity of the decisions made and enable an understanding behind catchment sensitivity to land-cover changes related to soil and catchment structure.Three metrics were selected to discretise the catchment into distinct areas for afforestation: the Topographic Wetness Index (TWI)28, Strahler27 and Shreve orders26. These metrics capture different parts of the catchment such as propensity for saturation, drainage network location and relative contributing areas. TWI is calculated by:$${{{{{mathrm{TWI}}}}}}=,{{{{mathrm{ln}}}}},frac{a}{tan ,gamma }$$ (17) where a is the upslope area draining through a point, per unit contour length, and γ is the local surface topographic slope in radians. All three metrics were calculated using the 50 m IHDTM60, thresholding stream formation at an accumulation of ten pixels using the D8 flow direction algorithm within ArcGIS 10.6.189. Strahler order ranges from one (headwaters) to seven (lowlands). Due to the continuous nature of TWI (0.05–31.49) and the large ordinal range of Shreve order (1–9523) calculated for the entire British Isles, we group TWI orders into five quantiles and seven quantiles for Shreve. Increasing TWI order in this case indicates increasing propensity for saturation, or potential maximum saturation level, and increasing Shreve order indicates increasing contributing area. Catchments were broken down to watersheds from the downstream point of the Shreve and Strahler orders. Due to the nature of the data, this led to some first order Strahler catchments being incorrectly generated for some catchments (Supplementary Table S7). Using these generated catchment areas, we plant both inside and outside of these watersheds to understand the hydrological difference between opposing planting locations. In each of the catchment areas, two different levels of afforestation were tested of ~25 and 50% of the possible planting area. Planted area was assigned at random in the catchment and was produced by calculating the area available for afforestation and randomly producing points that covered the area required using the Create Random Points tool in ArcGIS 10.6.1.Discussions exist about where to plant woodland in relation to existing land cover, to provide ecosystem services, including around watercourses29,30, urban areas31,32 and woodland4,33. Therefore, in this study we try to understand how these potential planting scenarios will affect hydrology in general. Using the CEH 2000 land-cover map56 buffers of broadleaf land cover were created at 25 and 50 m around these three land uses (Supplementary Fig. S7). These were then discretised according to the catchment areas. As an example, one scenario would be afforesting up to 50 m around existing broadleaf woodland inside the Shreve order one catchment area, whilst another would be randomly afforesting within 25% of the available area outside of TWI order five areas.Afforestation according to different catchment areas and land-cover uses between 234 and 288 scenarios for each catchment and between 0 and c. 40 percentage point increase in broadleaf woodland (Supplementary Fig. S2 and Table S8). Due to the structure and size of the different catchments, and thus differences in Strahler and Shreve orders, not all catchments had a comparable number of higher orders. Produced scenarios were converted to the 1-km2 grid scale by altering the fraction of land-cover types within each grid cell. It should be noted that this work only considers the impact of mature broadleaf woodland and neglects the influence of the initial planting and growing of the woodland that would likely have its own impact on catchment hydrology as frequently reported13,49. Furthermore, it does not include the period when there would be the highest amount of carbon sequestration. This study seeks to understand the theoretical impact of woodland on catchment hydrology when fully developed to understand the long-term implications of management decisions.Hydrological signatures and analysisSeveral hydrologic indices can be used to characterise the influence of afforestation on streamflow regime34,35. To analyse average streamflow and extremes, we look at the top 1% (very high flow), 5% (high flow), 50% (median flow), 90% (low flow) and 95% (very low flow) quantiles of daily streamflow. To quantify flow variability, we use the slope of the flow duration curve38,40 calculated thus:$${{{{{mathrm{FDC}}}}}}=frac{{{{{mathrm{ln}}}}}({Q}_{33 % })-,{{{{mathrm{ln}}}}}({Q}_{66 % })}{(0.66-0.33)}$$ (18) where Q33% is the 33rd flow exceedance quantile and Q66% is the 66th flow exceedance quantile. To ascertain catchment responsiveness to climatic forcing, we use median streamflow elasticity40,41:$${{{{{mathrm{MSE}}}}}}={{{{{mathrm{median}}}}}}left(frac{{{{{{mathrm{d}}}}}}Q}{{{{{{mathrm{d}}}}}}P}frac{P}{Q}right)$$ (19) where dQ and dP are the annual changes in yearly discharge and precipitation, respectively. Finally, we use the runoff ratio to quantify water balance changes related to streamflow and evapotranspiration42:$${{{{{mathrm{RR}}}}}}=frac{{mu }_{Q}}{{mu }_{P}}$$ (20) where µQ and µP are the average yearly discharge and precipitation using daily values, respectively. We also qualitatively assess the largest peak flow daily event in the 10-year record used in this study to determine the impact of afforestation on the highest possible flows in each catchment.To determine how afforestation influences streamflow metrics, percentage changes in flow metrics are plotted as a function of percentage point increases in afforestation (calculated using the difference between original and afforested scenario). Quantile regression is applied to determine the median regression slope of the trend for the entire period43. The benefit of using quantile regression is that it identifies the median response of the input variable (in this case the level of afforestation in both percentage and absolute terms) without being influenced by extreme outliers. In this way, we can estimate the proportional streamflow response to afforestation over the period. We use the regression slope coefficient as a proxy of catchment sensitivity to afforestation for each streamflow metric. The slope coefficient is then correlated to catchment attributes, as stated in the CAMELS-GB dataset44, using Spearman’s rank correlation. This allows us to determine the direction and significance of the catchment property influences on the sensitivity of catchments to afforestation for the different hydrologic signatures. To determine the impact of different planting locations according to catchment and land-cover location a one-way analysis of variance (ANOVA) test is undertaken using R90. More